I don't know much about the picture of Bickley but I am looking for the source that says it is him. In the book Shadow of the Sentinel (which is about 90% bull) has the picture credited to the author. That would make me doubt that it is Bickley. I have seen it credited to the Library of Congress in a real good article in North and South magazine called Strong Arm of Secession and the author is sending me information on the picture.
As far as the Masonic connection it is unknown if Bickley was a mason. Bickley received a letter while in prison from the doctor treating his wife and in it he states that he had heard Bickley was a brother mason but I have contacted the Grand Lodges of Texas, Ohio, Virginia, and Florida with no luck in finding his record. I took a list of known Texas KGC to the Grand Lodge of Texas and searched the returns for 1858-1865 and only about 1\4 were members of the craft.
If the picture is at the Library of Congress maybe we can get a better copy of it and see his insignia, kinda looks like the shaft of a cross with something over it.